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Higher descent equations based on 2-term $L_{\infty}$ algebras

Mengyao Wu, Danhua Song, Jie Yang

Abstract

In this paper, we develop the higher descent equations for higher gauge theories within the framework of 2-term $L_{\infty}$ algebras. Starting from a multilinear symmetric invariant polynomial, we construct a family of higher Chern-Simons type characteristic classes and verify that they satisfy the higher descent equations. These polynomials encode both the higher Chern-Weil theorem and the higher gauge anomalies.

Higher descent equations based on 2-term $L_{\infty}$ algebras

Abstract

In this paper, we develop the higher descent equations for higher gauge theories within the framework of 2-term algebras. Starting from a multilinear symmetric invariant polynomial, we construct a family of higher Chern-Simons type characteristic classes and verify that they satisfy the higher descent equations. These polynomials encode both the higher Chern-Weil theorem and the higher gauge anomalies.

Paper Structure

This paper contains 6 sections, 6 theorems, 67 equations.

Table of Contents

  1. Introduction
  2. 2-term L infty algebra connections and gauge transformation
  3. Balanced 2-term L infty algebra with invariant forms
  4. Higher descent equations based on the 2-term L infty algebra gauge theory
  5. Conclusion and outlook
  6. 2-term L infty algebra

Key Result

Proposition 3.1

Any non balanced 2-term $L_{\infty}$ algebra $\mathfrak{v}$, It can be minimally extended to a balanced 2-term $L_{\infty}$ algebra $\tilde{\mathfrak{v}}$.

Theorems & Definitions (12)

  • Definition 3.1
  • Proposition 3.1
  • Proposition 3.2
  • proof
  • Proposition 4.1
  • proof
  • Proposition 4.2
  • proof
  • Theorem 4.1
  • proof
  • ...and 2 more